Question

If f(x) = 2x - 2 and g(x) = 3x - 1, find (f - g)(4).
Answer

-17

5

-5

17

Answer 1

-5

Answer 2

Now why? Just giving the answer perhaps isn't very helpful.

The reason is
\[ (f-g)(x) = f(x) - g(x) \]
Now that being the case,
\[ (f-g)(4) = f(4) - g(4) \]

Hence you just need to evaluate f(4) and g(4), and then subtract one value from the other.

Answer 3

.-. what?

Answer 4

You want to find (f - g)(4). Now what does that mean?

It means the function f - g evaluated at 4.

So what does f - g mean as a function?

Well, the function f - g is defined as
\[ (f-g)(x) = f(x) - g(x) \]
Hence if you want to find (f-g)(4), then
\[ (f-g)(4) = f(4) - g(4) \]

Therefore to find the value of (f-g)(4), you need to find first
1. The value of f(4)
2. The value of g(4)
3. And then subtract them to find the value f(4) - g(4)

So step 1: given that f(x) = 2x - 2, it follows that
\[ f(4) = 2(4) - 2 = 8 - 2 = 6 \]

Now you do step 2 and step 3.

Answer 5

f(4) = 8-2=8-2=6
6=6

Answer 6

Step 2. What is the value of g(4), given that g(x) = 3x - 1?

Answer 7

g(4)= 3(4)-1
g(4)= 12 - 1
g(4)= 11

Answer 8

Right. Now, step 3, the value of (f-g)(4) is

f(4) - g(4) = .... what?